The advent of medical imaging of the anatomy's structure and function has allowed radiologists to view a patient's anatomy without the immediate need for invasive surgery. Transmission Tomography (TT), such as Computed Tomography (CT), allows the radiologist to view the patient's anatomical structure, while Emission Tomography (ET) allows the radiologist to view the patient's anatomical function. Positron Emission Tomography (PET) and Single Photon Emission Computed Tomography (SPECT) are common techniques for imaging anatomical function.
Typically, a SPECT system acquires the image data from photons radiated from a subject that has been injected with a radioactive tracer that radiates photons. A rotating gamma camera commonly acts as the recipient of the photons. Before the photons reach the rotating gamma camera, however, the photon pass through a collimator, which rotates with the camera and ensures that the camera only records photons that pass perpendicular to the camera lens. Various collimators exist in photons that pass perpendicular to the camera lens. Various collimators exist in practice, such as varying focal-length fan-beam (VFF) collimators, parallel-hole (PH) collimators, fan-beam (FB) collimators, fixed focal-length fan-beam collimators, parallel-beam collimators, and varying focal-length cone-beam collimators. Each collimator geometry has a unique performance capability with distinct advantages and disadvantages, making some collimators more favorable than others when imaging a particular anatomical function. For instance, as compared to the FB geometry, the VFF geometry, with an equivalent spatial resolution, improves signal-to-noise ratio and acquires more counts from regions where the FB collimations encounters truncation. Depending on the selected collimator, the image produced by the camera may vary.
Once the photon passes through the collimator and the camera receives and records the photon, a processor reconstructs the received data to create a reconstructed three dimensional (3D) image of the subject. Typically, a processor algorithm is used to transform the camera's emission data to generate a 3D image. A common algorithm used in SPECT image reconstruction is the iterative maximum likelihood expectation maximization (ML-EM) reconstruction algorithm with the ordered-subsets (OS) strategy, the combination of which is commonly referred to as the OS-EM algorithm. There are three parts to the OS-EM algorithm: (1) iterative re-projection of the volume at each angle for the projection image, (2) iterative back-projection of the projection data, and (3) grouping of the detector bins in the camera. Although the OS-EM algorithm achieves a good quantitative reconstruction, there are limitations in clinical use. One drawback is the high computational cost of the algorithm resulting from the large vectors and matrices associated with producing a high-resolution image reconstruction. Research efforts have been devoted to mitigate this drawback by (1) developing efficient simulators for the re-projection and back-projection cycle, such as by the use of the geometry warping with distance-dependent convolution or the recursive ray-tracing with geometry symmetries; and (2) investigating sophisticated strategies to speedup the convergence to a satisfactory result, such as the OS technique. Although a significant speed gain was observed by the addition of the OS technique, the reconstruction time is still typically too long for acceptable clinical use. Improved techniques for image reconstruction for SPECT images are desired.